This is a competing proposal for applied statistical research motivated by environmental studies, both in humans and animals, and related to carcinogenicity, teratology and other health outcomes. Specific aims are: 1) Time to event analyses for data arising from complex pregnancy and birth cohorts; 2) Statistical models for high dimensional covariates and outcomes; 3) Improved methods for dose response modeling for the purpose of quantitative risk assessment; 4) Goodness of fit for general linear mixed models. Empirical data analysis will play a central role in achieving the specific aims. In addition to addressing important real world questions motivated by environmental risk assessment, the proposed research offers useful contributions to general statistical methodology in survival analysis, clustered data methods, hierarchical modeling and analysis of multiple outcomes. Both Bayesian and frequentist approaches will be used.